The probability that a city bus is ready for service when needed is 84%. The probability that a city bus is ready for service and has a working radio is 67%. Find the probability that a bus chosen at random has a working radio given that is it ready for service.

a. 17.0%
b. 79.8%
c. 83.8%
d. 12.5%

1 answer

To find the probability that a bus chosen at random has a working radio given that it is ready for service, we use the formula for conditional probability:

P(working radio | ready for service) = P(working radio and ready for service) / P(ready for service)

P(working radio | ready for service) = 0.67 / 0.84 = 0.797619

Therefore, the probability that a bus chosen at random has a working radio given that is ready for service is approximately 79.8%, which is option b.